What is the volume of the cube shown?

6 3/4
11 25/64
30 3/8
8 1/64

Please help !

Answer:

DQ = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}[/tex]

Step-by-step explanation:

Given function is f(x) = [tex]\frac{5}{2-\sqrt{x}}[/tex]

f(x + h) = [tex]\frac{5}{2-\sqrt{x+h} }[/tex]

Therefore, indicated difference quotient will be,

DQ = [tex]\frac{f(x+h)-f(x)}{h}[/tex]

Now we substitute the values in the difference quotient,

DQ = [tex]\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}[/tex]

      = [tex]\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

This is basically saying [tex]1 \le x < 4[/tex]

The square bracket says "include this endpoint" while the curved parenthesis means "exclude this endpoint". We can tell what is included/excluded based on how the endpoint is drawn.

Open circle = exclude endpoint

Closed/filled in circle = include endpoint

Your teacher has also drawn a square bracket at the left endpoint, and a curved parenthesis at the right endpoint. This style of drawing the endpoints helps set up [1, 4). Though sometimes you might see the use of open/closed circles instead for the endpoints. I'm referring to the number line portion.

We want to express the shaded set of numbers on the x-axis with interval notation.

The interval notation is:

[1, 4)

Let's start by analyzing the graph.

We have two ends, one at x = 1, with a colored dot, which means that that value belongs to the set.

We have the other end at x = 4, with a white dot, which means that the value does not belong to the set.

Then the interval notation is:

[1, 4)

Where [] are used for colored dots.

() are used for white dots.

If you want to learn more, you can read:

https://brainly.com/question/16768997

I have attached the complete question.

Answer:

See 2nd attachment

Step-by-step explanation:

We are told that R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y = 3.

Thus, the region in the xz plane would be defined as;

0 ≤ x ≤ 3 and x² ≤ z ≤ 5x

For the iterated integral for the volume of the solid R, see 2nd attachment.

Answer:

The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].

Hence,

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]

Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]

Midpoint = [tex](5, 5, 4)[/tex]

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]

[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]

[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]

[tex]d = \sqrt{16 +196 + 0[/tex]

[tex]d =\sqrt{212}[/tex]

[tex]d = 2\sqrt{53}[/tex]

This is the diameter

To find the radius, r

From [tex]Radius = \frac{Diameter}{2}[/tex]

[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]

∴ [tex]Radius = \sqrt{53}[/tex]

r = [tex]\sqrt{53}[/tex]

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is [tex](5, 5, 4)[/tex]

Radius of the sphere is [tex]\sqrt{53}[/tex]

The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by

[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]

Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

This is the standard equation of the sphere

Answer:

x = -7

Step-by-step explanation:

This isn't a quadratic.

Step 1: Write out equation

3x - 5 = -26

Step 2: Add 5 to both sides

3x = -21

Step 3: Divide both sides by 3

x = -7

Step-by-step explanation:

[tex]\sf \bf We \: have,[/tex]

[tex]\sf 3x - 5 = -26[/tex]

[tex]\sf : \implies \bf 3x - 5 \green{+5}= -26\green{+5}[/tex]

[tex]\sf : \implies \bf 3x =-21[/tex]

[tex]\sf : \implies \bf 3x× \green{\dfrac{1}{3}}=-21× \green{\dfrac{1}{3}}[/tex]

[tex]\sf : \implies \bf \underline{\boxed{\sf \bf x = -7}}[/tex]

Answer:

m=(y2-y1)/(x2-x1)

=(2-6)/(6-2)

=-4/4

=-1

Step-by-step explanation:

Answer: It’s the second one

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-13 - 7)/(-1 + 3) = -20/2 = -10

y - 7 = -10(x - 3)

y - 7 = -10x + 30

y =  - 10x + 37

Answer:

25 0r 26 F

Step-by-step explanation:

around .5 - 1 C

Answer:

600 %

Step-by-step explanation:

x · 150 ÷ 100 = 900

150x = 90000

x = 600

Answer:

14-2i

Step-by-step explanation:

[tex]\left(3+5i\right)+\left(11-7i\right)\\\\Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number\\\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3+11\right)+\left(5-7\right)i\\3+11=14\\5-7=-2\\\\=14-2i[/tex]

Answer:

So in this sequence, we are adding by 9 in each term

So our pattern is: 7 , 7 +9 , 7 + 2(9) , 7 + 3(9) .....

hence, we can write it as: 7 + [tex]9^{n-1}[/tex] where n is the number of the term you want

Answer:

LET ME GUESS hmmmm... OH WAIT 30

Step-by-step explanation:

Answer:

30 ft

Step-by-step explanation:

The elm tree is 3 times as tall as the apple tree.

The elm tree is 3 times as tall as 10 ft.

3 * 10 ft = 30 ft

Answer:

A. 3-5= -2, which is not a counting number.

Step-by-step explanation:

Counting numbers are non negative numbers greater than 1 up to infinity. Counting numbers are also called natural numbers, and they do not include the negative numbers.

The statement states that "The difference of any two counting numbers will be a counting number"

From option A we can disprove that, since we can see that not all the difference between two counting numbers gives a counting number.

3 is a counting number

5 is a counting number

The difference between 3 and 5 gives -3, which is not a counting number.

This is a counterexample to the statement above.

The correct answers are Planet A 16 hours - Inner planet and planet B 1,408 hours - Outer planet.

Large, circular celestial objects that are neither stars nor their remnants are known as planets. The inner planets are the ones that are much closer to the sun, thus they have much smaller orbits around it and it takes them much less time to circle around it. Also, these planets are much smaller, which enables them to spin around their axis much quicker too, so one day passes much quicker.

The outer planets are the total opposite. They are much further from the sun, so for them to be able to make a single circle around the sun it takes much more time, and also because they are much bigger, it takes them much more time to spin around their own axis, thus making one day much longer than the days of the inner planets.

The complete question is given below as:-

Which planet is an inner planet, and which one is an outer planet? Explain your answer. Planet A 16 hours planet B 1,408 hours

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The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Let's say the original price of the mobile is x.

12% of x is 0.12x

The cost of refurbished mobile will be as x - 0.12x = 0.88x

0.88x = 572

x = $650

The amount saved = $650 - $572 = $78

Hence "The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile".

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Answer:

The parametric equations are

 x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4

Step-by-step explanation:

Step(i):-

Given point P = ( 4,2,4)

Given vector is   -2 i - 5 j - 3 k

The vector equation of a line through the point a⁻ and parallel to b⁻ is

r⁻ = a⁻ + t b⁻  

Given r⁻ = 4 i + 2 j + 4 k

r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)

Step(ii):-

The Cartesian form

[tex]\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t[/tex]

[tex]\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t[/tex]

[tex]\frac{x-4 }{-2 } = t[/tex]

⇒ x - 4 = -2 t

⇒ x = - 2 t + 4

[tex]\frac{y-2 }{-5 } = t[/tex]

⇒ y - 2 = - 5 t

⇒ y = - 5 t + 2

[tex]\frac{z-4 }{-3 } = t[/tex]

z - 4 = -3 t

z = - 3 t + 4

Conclusion:-

The parametric equations are

 x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4

Answer:

358 toys sold 11 months after the first year.

Step-by-step explanation:

y = - 2x + 380

x is number of months after release in this case x = 11

y is number of toy sold in the hundreds.

y = - 2 ( 11 ) + 380

y = - 22 + 380

y = 358

Number of toys sold 11 months after the first year =  358

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Given,

Linear equation

y = - 2x + 380

x is number of months after release

y is number of toy sold in the hundreds.

No. of months, x = 11

Putting value of x in above equation

y = - 2 ( 11 ) + 380

y = - 22 + 380

y = 358

Hence, 358 toys sold 11 months after the first year.

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The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula . What transformations are used in transforming the parent graph y = x, to obtain the graph of blank. The answers would be:

To obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given function of temperature is c(x) = (5/9){ x - 32}. The two graphs are plotted on the x-y plane. It is observed that y = x is transformed to the horizontal direction.

The graph of the two functions y = x and c(x) = (5/9){ x - 32 } is attached with the answer below.

Therefore, to obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

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Answer:

64 Divided by 8

Step-by-step explanation:

Answer:

The answer is 18.

Step-by-step explanation:

You just need to plug in -7 to the equation 2x-4. You get -18, but absolute value is always positive, so its 18.

The answer is 18.

Sorry no explanation im soooo sorry

Answer:

11

Step-by-step explanation:

sawarasenaaa kimi wa-

Hi there!

~

[tex]18[/tex]% [tex]= \frac{9}{50}[/tex]

Answer9/50:

Step-by-step explanation:

18/100

18÷2

100÷2

9/50

Answer:$12

Step-by-step explanation:

Answer:

months of game play (m) =$11

Step-by-step explanation:

Answer:

10+(n/2)=6

Step-by-step explanation:

Let the number be n

Quotient of n and 2 is (n/2)

Sum of this and 10 is

10+(n/2)=6

Answer:

the answer is 200

Step-by-step explanation:it's because

you have to divide 1000 in to 5 and 1000 divided by 5 is 200